Strict Convexity of Some Subsets of Hankel Operators

By Caixing Gu and Jonathan E. Shapiro

This paper appears in the Proceedings of the American Mathematical Society, Volume 131, Number 9 (2003), 2779-2789.
You can see it on their web site here.

Abstract:

We find some extreme points in the unit ball of the set of Hankel operators and show that the unit ball of the set of compact Hankel operators  is strictly convex.  We use this result to show that the collection of NxN lower triangular Toeplitz contractions is strictly convex.  We also find some extreme points in certain reduced Cowen sets and discuss cases in which they are or are not strictly convex.

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